Question

there is a right - angled triangle (the right angle is marked). one of the legs is 19, the other leg is labeled as f, and one of the acute angles is 52 degrees. there is also a number 10 in another cell, but it seems not related to this triangle problem for now.

Explanation:

Step1: Identify trigonometric ratio

We use tangent: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$
Here, $\theta=52^\circ$, opposite side $=19$, adjacent side $=f$.

Step2: Rearrange to solve for $f$

$f=\frac{19}{\tan(52^\circ)}$

Step3: Calculate the value

First, $\tan(52^\circ)\approx1.2799$, so $f\approx\frac{19}{1.2799}\approx14.84$

Answer:

$\approx14.84$